Question

Find the measure of ∠ABC. Show your work.

Answer 1

Answer : The measure of ∠ABC is, 96°

Step-by-step explanation :

As we know that an inscribed angle is half the measure of its intercepted arc.

As we are given that:

Intercepted arc = 192°

Now we have to determine the inscribed angle ∠ABC.

According to property:

`\text{Inscribed angle }\angle ABC=\frac{\text{Intercepted arc}}{2}`

`\text{Inscribed angle }\angle ABC=(192^o)/(2)`

`\text{Inscribed angle }\angle ABC=96^o`

Therefore, the measure of ∠ABC is, 96°

Answer 2

81°

Explanation:

Points A, B and C lie on the circle. A and C are endpoints, B is the vertex of the angle ABC. Angle ABC is inscribed angle subtended on the arc AC with measure 192°.

The measure of the inscribed angle subtended on the arc is half the measure of the central angle subtended on the same arc. The measure of the central angle is the same as the measure of the arc, so

`m\angle ABC=(1)/(2)\cdot 192^(\circ)=81^(\circ)`